Many homes in the five boroughs of New York City, like these brownstones in Brooklyn, are out of budget range for first-time home buyers. Photo Credit: iStock

Home ownership is turning into an impossible dream for many New Yorkers trying to raise families and cope with rising prices, debt and a challenging job market.

It's tough to get traction in a city where the median income of $50,886 has remained almost flat since 2000 and 30 percent of residents pay more than half their incomes for rent -- a "severe burden," according to federal standards cited in a report by City Comptroller John C. Liu.

But the current squeeze is exacerbated by several trends, said Philip Kasinitz, a sociology professor at CUNY Graduate Center: rising rents and fewer rent-regulated apartments; increasing numbers of affluent people who once migrated to the suburbs but now wish to raise kids in Manhattan; and more parents wishing to escape private school costs by moving to neighborhoods with good public schools.

Areas in the outer boroughs may have family friendly housing, Kasinitz noted, but many are in areas with inferior schools.

Nationally, households headed by adults under 35 had 68 percent less wealth than their same-aged counterparts had in 1984, according to a 2011 Pew Research study. The same study showed the number of households headed by adults under 35 with incomes below the poverty line almost doubled from 1967 to 2010, going from 12 percent to 22 percent.

The home-owning picture for young people is especially grim in New York, where many are trapped by high rents that don't allow them to save for a down payment on a home.

"We live hand to mouth, pretty much. It's robbing Peter to pay Paul," said Zoila Sylvester, 28, a marketing director for Mayimba Music and a renter in Carroll Gardens in Brooklyn.

Having given up on being able to afford a home to buy, she dreams of finding a large, rent-regulated apartment.

How to have a family in the city where she grew up, "is something I stress over all the time," said writer Nona Willis Aronowitz, 28.

Aronowitz, who rents an apartment in Crown Heights, Brooklyn, with her husband, an independent filmmaker, is working on a book called "Generation Crash" about the diminished possibilities facing people her age.

"I feel kind of indignant, like, 'You're not going to push me out of my own city!' " Aronowitz said.

Prices of three-bedroom homes of all types in the city increased 14 percent to $418,800 from February 2003 to December 2012, according to the Zillow Home Value Index, but the devil in the increases is in the details. Manhattan three-bedroom homes increased 525 percent since September 1997, from $400,200 to $2.5 million.

Two-bedroom homes in Brooklyn rose 12 percent -- from $465,300 in April 2005 to $521,300 in December 2012. But homes in high-demand neighborhoods with great schools and low crime rates easily command millions, Realtors said.

"There is a lot of frustration" among prospective buyers, said Elizabeth Kohen, a broker at Garfield Realty, which specializes in Brooklyn neighborhoods such as Park Slope.

Many want to take advantage of low interest rates right now, but "the buyers who have all cash and have a substantial amount to put down are the ones who wind up owning," Kohen said. The market right now "is on fire," with young couples often being staked to their first homes by affluent, older relatives, Kohen said.

"You can't get an apartment for less than $300,000 and for that price you can't raise a family in it," said Aislinn Forbes, 28, of Brooklyn Heights.